Exercises
[07B]Prerequisites:[078].(Proposed on 2022-10-13) Show that if for the total ordering of \(X\) all ”suprema” exist then all ”infima” also exist; and vice versa. Precisely, show that these are equivalent:
Every non-empty set bounded from below in \(X\) admits greatest lower bound;
every non-empty set bounded from above in \(X\) admits least upper bound.
Solution 1